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Mean-Variance Hedging and Numéraire

Author

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  • Christian Gourieroux
  • Jean Paul Laurent
  • Huyên Pham

Abstract

We consider the mean-variance hedging problem when the risky assets price process is a continuous semimartingale. The usual approach deals with self-financed portfolios with respect to the primitive assets family. By adding a numéraire as an asset to trade in, we show how self-financed portfolios may be expressed with respect to this extended assets family, without changing the set of attainable contingent claims. Copyright Blackwell Publishers Inc 1998.

Suggested Citation

  • Christian Gourieroux & Jean Paul Laurent & Huyên Pham, 1998. "Mean-Variance Hedging and Numéraire," Mathematical Finance, Wiley Blackwell, vol. 8(3), pages 179-200.
  • Handle: RePEc:bla:mathfi:v:8:y:1998:i:3:p:179-200
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    1. repec:gam:jrisks:v:5:y:2017:i:3:p:36-:d:105112 is not listed on IDEAS
    2. Kohlmann, Michael & Tang, Shanjian, 2002. "Global adapted solution of one-dimensional backward stochastic Riccati equations, with application to the mean-variance hedging," Stochastic Processes and their Applications, Elsevier, vol. 97(2), pages 255-288, February.
    3. Michael Mania & Revaz Tevzadze, 2008. "Backward Stochastic PDEs Related to the Utility Maximization Problem," ICER Working Papers - Applied Mathematics Series 07-2008, ICER - International Centre for Economic Research.
    4. Anne Eyraud-Loisel, 2013. "Quadratic hedging in an incomplete market derived by an influent informed investor," Post-Print hal-00450949, HAL.
    5. Goutte, Stéphane & Ngoupeyou, Armand, 2015. "The use of BSDEs to characterize the mean–variance hedging problem and the variance optimal martingale measure for defaultable claims," Stochastic Processes and their Applications, Elsevier, vol. 125(4), pages 1323-1351.
    6. repec:dau:papers:123456789/12663 is not listed on IDEAS
    7. Liao Wang & Johannes Wissel, 2013. "Mean-variance hedging with oil futures," Finance and Stochastics, Springer, vol. 17(4), pages 641-683, October.
    8. Jean -Luc Prigent & Olivier Renault & Olivier Scaillet, 1999. "An Autoregressive Conditional Binomial Option Pricing Model," Working Papers 99-65, Center for Research in Economics and Statistics.
    9. Claudio Fontana, 2013. "Weak and strong no-arbitrage conditions for continuous financial markets," Papers 1302.7192, arXiv.org, revised May 2014.
    10. Kramkov, D. & Sîrbu, M., 2007. "Asymptotic analysis of utility-based hedging strategies for small number of contingent claims," Stochastic Processes and their Applications, Elsevier, vol. 117(11), pages 1606-1620, November.
    11. Stephane Goutte & Armand Ngoupeyou, 2012. "Optimization problem and mean variance hedging on defaultable claims," Papers 1209.5953, arXiv.org.
    12. Wanyang Dai, 2014. "Mean-variance hedging based on an incomplete market with external risk factors of non-Gaussian OU processes," Papers 1410.0991, arXiv.org, revised Aug 2015.
    13. L. Carassus & E. Temam, 2014. "Pricing and hedging basis risk under no good deal assumption," Annals of Finance, Springer, vol. 10(1), pages 127-170, February.
    14. Dorival Le~ao & Alberto Ohashi & Vinicius Siqueira, 2013. "A general Multidimensional Monte Carlo Approach for Dynamic Hedging under stochastic volatility," Papers 1308.1704, arXiv.org, revised Aug 2013.
    15. Vicky Henderson & David Hobson & Sam Howison & Tino Kluge, 2003. "A Comparison of q-optimal Option Prices in a Stochastic Volatility Model with Correlation," OFRC Working Papers Series 2003mf02, Oxford Financial Research Centre.
    16. Woll, Oliver, 2015. "Mean-risk hedging strategies in electricity markets with limited liquidity," ZEW Discussion Papers 15-056, ZEW - Zentrum für Europäische Wirtschaftsforschung / Center for European Economic Research.

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